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INTRODUCTION

This document offers a detailed overview of key mathematical concepts, including linear and quadratic equations, determinants, and solutions for simultaneous equations. It also explores trigonometric functions, important identities, and properties of triangles. Additionally, the guide includes a discussion on the rectangular coordinate system, points, symmetry, projection, scalar components, distance between points, and direction cosines of a segment. This resource is essential for students and educators seeking to enhance their understanding of algebra and geometry.

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INTRODUCTION

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  1. INTRODUCTION Some Preliminaries Concepts

  2. Some preliminaries concept • Linear Equation • Quadratic Equation • Exponent • Logarithms • Determinants

  3. Solution of two simultaneous first degree equations in two unknowns • The general form : • The solutions are x and y that satisfy both equations • Ex: solve this equation!

  4. Solution of three simultaneous first degree equations • The general form: • Example: find the value of x, y and z from these simultaneous equation :

  5. Trigonometry • The trigonometric functions • The trigonometric functions for special angles • Important identities • Relations for triangles • Inequality and absolute value

  6. The Point and Plane Vectors FaridaNurhasanah

  7. 2-2. The Rectangular Coordinate System • A Point is an undefined object which we shall represent pictorially by a dot • Coordinates of point are two real number that represent the distance of the point from axis of abscissa and ordinate. It is represent by (x,y) • (See demonstration using GSP)

  8. 2-3. Symetry • A Point can be symmetric to a point and to a line

  9. 2-4. Projection • The projection of a point on a given line is the foot of the perpendicular dropped from the point to the line

  10. 2-5. Scalar Components of a segment • Let and Then the scalar component of AB can be write as [∆X, ∆Y] in which: • Example : back to previous GSP

  11. 2-6. Distance between Two Points • Try to find the distance between point A and B from the previous example!

  12. 2-7. Direction Cosines of a Segment • Let and any two distinct points in the plane • The direction cosine of AB are defined to be the cosine of the angles between AB and the rays, or half-lines, through A parallel to the positive x-axis and positive y-axis, respectively

  13. Ilustration

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